x = np.linspace(-2.5, 2.5, 1000)
# The parametrized function to be plotted
def f(x, beta, c):
return 1 / 4 * x**4 - x**2 - c * x
# Define initial parameters
u_bounds = np.array([[-2, 2]])
x_bounds = np.array([[-1.5, 1.5]])
#bounds_u = np.array([u_bounds])
u_boxes = np.array([20])
x_boxes = np.array([15])
Omega_u = domain.discretization(u_bounds, u_boxes)
Omega_x = domain.discretization(x_bounds, x_boxes)
# I think X and U need to be generated in a different way
X = Omega_x.randPerBox(100)
# U = np.random.uniform(u_bounds[0], u_bounds[1], (1, X.shape[1]))
U = Omega_u.randPerBox(100)
dim_x = X.shape[0]
dim_u = U.shape[0]
Y = s.b(X[:, 0])
Z = s.sigma(X[:, 0])
#%% Define observables
order = 6
phi = observables.monomials(order)
psi = observables.monomials(order) #lambda u: np.array([1])
sys.path.append('../../')
import klus_algos as algorithms
import domain as domain
import observables as observables
import systems as systems
from tools import printVector, printMatrix
plt.ion()
#%% Simple deterministic system -------------------------------------------------------------------
# define domain
bounds = np.array([[-2, 2], [-2, 2]])
boxes = np.array([50, 50])
Omega = domain.discretization(bounds, boxes)
# define system
gamma = -0.8
delta = -0.7
def b(x):
return np.array([gamma * x[0, :], delta * (x[1, :] - x[0, :]**2)])
# define observables
psi = observables.monomials(8)
# generate data
X = Omega.rand(1000) # generate test points
import matplotlib
import matplotlib.pyplot as plt
from matplotlib.widgets import Slider
import sys
sys.path.append('../../')
import domain
import estimate_L
import observables
import utilities
#%% Define domains
x_bounds = np.array([[-2, 2], [-1.5, 1.5]])
x_boxes = np.array([20, 15])
x_omega = domain.discretization(x_bounds, x_boxes)
u_bounds = np.array([[-2, 2]])
u_boxes = np.array([300])
u_omega = domain.discretization(u_bounds, u_boxes)
#%% Define system
def b(x, u):
return np.vstack([-4 * x[0, :]**3 + 4 * x[0, :], -2 * x[1, :]]) + u
def sigma(x):
n = x.shape[1]
y = np.zeros((2, 2, n))
y[0, 0, :] = 0.7
